[sdiy] SVFs with different gains in the integrators
Richie Burnett
rburnett at richieburnett.co.uk
Tue Dec 15 19:26:56 CET 2020
The Just Noticeable Difference for Q is quite large because it only influences the amplitude of a handful of spectral components around the cutoff frequency. JNDs for cutoff frequency or overall amplitude variation are much smaller because they influence more of the signal's spectrum, so have a greater perceived effect.
-Richie,
Sent from my Xperia SP on O2
---- Tom Wiltshire wrote ----
>
>
>> On 15 Dec 2020, at 13:24, Guy McCusker <guy.mccusker at gmail.com> wrote:
>>
>>> This simply implies that the denominator of a S-V filter changes from a normalized s^2 +(1/Q)s + 1 to s^2 + (A1/Q)s + A1A2 where the integrator gains change from 1 to A1 and A2 respectively, -1/Q is feedback VB to input, and the feedback from VL to input is -1. Just a modified 2nd-order, and the quadratic equation yields the exact new poles (hence the exact SHAPE of the frequency response) and corresponding (re-interpreted?) performance parameters. [For example, Omega-Zero moves from 1 to sqrt(A1A2) as someone here offered.] Everything should follow easily, obviously, and correctly. No magic in this - right?
>>
>>
>> I guess the interesting -- though admittedly not magical -- element of
>> this to me is that the Q of the transfer function you have written is
>> not given by the parameter called Q but by Q * sqrt(A2/A1), so the Q
>> of the filter is influenced by the ratio of the integrators' unity
>> gain frequencies as well as by the feedback from the bandpass. Andrew
>> Simper pointed out that this is also relevant to standard
>> implementations because presumably the two integrators are not
>> perfectly matched, though I suppose the influence of their mismatch is
>> not that great.
>
>The square root helps makes sure it’s not that significant.
>
>Imagine A1 and A2 are out by up to 10% so the worst case is either
>
>1.1/0.9 = 1.22, sqrt(1.22) = 1.105
>
>0.9/1.1 = 0.81, sqrt(0.81) = 0.90
>
>So a 10% variation in the integrator frequencies (both of them) gives a 10% variation in Q. That’s not that huge in Q terms, and we might hope that we get closer matching between our integrators than 10%.
>
>Tom
>
>
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